PreprintarXiv licencearXiv
On complete Ricci--flat Kähler manifolds
Abstract
We study complete noncompact Ricci-flat Kähler manifolds. In the case of Euclidean volume growth, we prove that the underlying complex manifold is naturally quasi-projective and that the asymptotic cone is unique. Moreover, we establish no semistability at infinity and prove convergence to the asymptotic cone at a polynomial rate. In the case of sub-Euclidean volume growth, we construct complete Ricci-flat Kähler threefolds with bounded sectional curvature and finite topological type that admit no Kähler compactification.
Related
- Instability of the Fundamental Group for Ricci-Flat Kähler 4-Manifolds
- Hamiltonian stationary Lagrangian currents in Ricci-flat Kähler manifolds
- Complete Kähler Manifolds with pinched Ricci curvature
- Ricci pinching on complete Kähler manifolds with nonnegative bisectional curvature
- Ricci pinching on complete Kahler manifolds
BibTeX
@misc{sun2026complete,
title = {{On complete Ricci--flat Kähler manifolds}},
author = {Song Sun and Junsheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29891},
eprint = {2610.29891},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29891},
}
RIS
TY - UNPB
TI - On complete Ricci--flat Kähler manifolds
AU - Song Sun
AU - Junsheng Zhang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29891
UR - https://arxiv.org/abs/2610.29891
AB - We study complete noncompact Ricci-flat Kähler manifolds. In the case of Euclidean volume growth, we prove that the underlying complex manifold is naturally quasi-projective and that the asymptotic cone is unique. Moreover, we establish no semistability at infinity and prove convergence to the asymptotic cone at a polynomial rate. In the case of sub-Euclidean volume growth, we construct complete Ricci-flat Kähler threefolds with bounded sectional curvature and finite topological type that admit no Kähler compactification.
ER -